Question

Next-door neighbors Bob and Jim use hoses from both houses to fill Bob’s swimming pool. They know that it takes 18 h using both hoses. They also know that Bob’s hose, used alone, takes 20% less time than Jim’s hose alone. How much time is required to fill the pool by each hose alone?

Short answer

The time required for Jim’s hose is 40.5 hours and time for bob’s hose is 32.4 hours.

Step-by-step solution

Step-1. Determine the quantities.

Let t be the time taken by Jim hose to fill the pool.

Thus, in one hour Jim can fill$\frac{1}{t}$ th part of the pool.

Bob takes 20% less time thus, $t-0.2t=0.8t$.

In one hour, Bob can fill $\frac{1}{0.8t}$th part of the pool.

Together they take 18 hours.

In one hour, they can fill $\frac{1}{18}$th part of the pool.

Step-2. Set up the model.

The sum of their individual rates is equal to their rates working together.

$\begin{array}{l}\frac{1}{t}+\frac{1}{0.8t}=\frac{1}{18}\\ \frac{1}{t}+\frac{5}{4t}=\frac{1}{18}\end{array}$

Step-3. Solve for t.

$\begin{array}{l}\frac{1}{t}+\frac{5}{4t}=\frac{1}{18}\\ \frac{4+5}{4t}=\frac{1}{18}\\ 9\times 18=4t\\ t=40.5\end{array}$

The time taken by Jim hose to fill the pool is 40.5 hours.

Time for Bob’s hose in hours is

$40.5\times 0.8=32.4$

Hence, the time required for Jim’s hose is 40.5 hours and time for bob’s hose is 32.4 hours.